Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort
Abstract
We have shown that there is a link between the geometry of the CA II-nM’s with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.
Keywords:
Antiprism / Deltahedron / Concave / RingSource:
GEOMETRIAS’19: BOOK OF ABSTRACTS, 2019, 89, 85-Publisher:
- Porto: Aproged - Associação dos Professores de Geometria e de Desenho
Funding / projects:
- Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-44006)
Note:
- GEOMETRIAS’19: POLYHEDRA AND BEYOND | PORTO | 05 - 07 SEPTEMBER 2019. http://www.aproged.pt/geometrias19/g19bookofabstracts.pdf?fbclid=IwAR1KxpRVvWZlDD-LkfPC-lWFk6jAs7ZQn5Kz5EDJpdx2chDGOKzgG1xD-uE
Collections
Institution/Community
GraFarTY - CONF AU - Obradović, Marija AU - Mišić, Slobodan PY - 2019 UR - https://grafar.grf.bg.ac.rs/handle/123456789/1982 AB - We have shown that there is a link between the geometry of the CA II-nM’s with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research. PB - Porto: Aproged - Associação dos Professores de Geometria e de Desenho C3 - GEOMETRIAS’19: BOOK OF ABSTRACTS T1 - Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort SP - 85 VL - 89 DO - 10.24840/978-989-98926-8-2 ER -
@conference{ author = "Obradović, Marija and Mišić, Slobodan", year = "2019", abstract = "We have shown that there is a link between the geometry of the CA II-nM’s with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.", publisher = "Porto: Aproged - Associação dos Professores de Geometria e de Desenho", journal = "GEOMETRIAS’19: BOOK OF ABSTRACTS", title = "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort", pages = "85", volume = "89", doi = "10.24840/978-989-98926-8-2" }
Obradović, M.,& Mišić, S.. (2019). Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS Porto: Aproged - Associação dos Professores de Geometria e de Desenho., 89, 85. https://doi.org/10.24840/978-989-98926-8-2
Obradović M, Mišić S. Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS. 2019;89:85. doi:10.24840/978-989-98926-8-2 .
Obradović, Marija, Mišić, Slobodan, "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort" in GEOMETRIAS’19: BOOK OF ABSTRACTS, 89 (2019):85, https://doi.org/10.24840/978-989-98926-8-2 . .